Abstract
Warp of cross sections of square section bars in torsion is reduced in Cosserat elasticity in comparison with classical elasticity. Warp is observed experimentally to be substantially reduced, by about a factor of four compared with classical elasticity, in an open-cell polymer foam for which Cosserat elastic constants were previously determined. The observed warp in the foam is consistent with a prediction based on Cosserat elasticity. Concentration of strain in the foam is therefore reduced in comparison with classical elasticity.
Article PDF
Avoid common mistakes on your manuscript.
References
Sokolnikoff I.S.: Theory of Elasticity. Krieger, Malabar, FL (1983)
Cosserat E., Cosserat F.: Theorie des Corps Deformables. Hermann et Fils, Paris (1909)
Mindlin R.D.: Stress functions for a Cosserat continuum. Int. J. Solids Struct. 1, 265–271 (1965)
Mindlin R.D.: Effect of couple stresses on stress concentrations. Exp. Mech. 3, 1–7 (1963)
Eringen A.C.: Theory of micropolar elasticity. In: Liebowitz, H. (ed) Fracture, 1, pp. 621–729. Academic Press, New York (1968)
Park H.C., Lakes R.S.: Torsion of a micropolar elastic prism of square cross section. Int. J. Solids, Struct. 23, 485–503 (1987)
Anderson W.B., Lakes R.S., Smith M.C.: Holographic evaluation of warp in the torsion of a bar of cellular solid. Cellular Polymers 14, 1–13 (1995)
Lakes R.S., Gorman D., Bonfield W.: Holographic screening method for microelastic solids. J. Mater. Sci. 20, 2882–2888 (1985)
Lakes R.S.: Experimental microelasticity of two porous solids. Int. J. Solids Struct. 22, 55–63 (1986)
Anderson W.B., Lakes R.S.: Size effects due to Cosserat elasticity and surface damage in closed-cell polymethacrylimide foam. J. Mater. Sci. 29, 6413–6419 (1994)
Mora R., Waas A.M.: Measurement of the Cosserat constant of circular cell polycarbonate honeycomb. Philos. Mag. A 80, 1699–1713 (2000)
Sikon M.: Theory and experimental verification of thermal stresses in Cosserat medium. Bull. Polish Acad. Sci. Tech. Sci. 57(2), 177–180 (2009)
Rueger Z., Lakes R.S.: Experimental Cosserat elasticity in open cell polymer foam. Philos. Mag. 96(2), 93–111 (2016)
Foamade Industries, Auburn Hills, MI
Peters W.H., Ranson W.F.: Digital imaging techniques in experimental stress analysis. Opt. Eng. 21, 427–431 (1982)
Lecompte D., Smits A., Bossuyt S., Sol H., Vantomme J., Van Hemelrijck D., Habraken A.M.: Quality assessment of speckle patterns for digital image correlation. Opt. Lasers Eng. 44, 1132–1145 (2006)
Wang Y., Cuitino A.M.: Full-field measurements of heterogeneous deformation patterns on polymeric foams using digital image correlation. Int. J. Solids Struct. 39, 3777–3796 (2002)
Chen C.P., Lakes R.S.: Holographic study of non-affine deformation in copper foam with a negative Poisson’s ratio −0.8. Scripta Metall Mater. 29, 395–399 (1993)
Gibson, L.J., Ashby, M.F.: Cellular Solids, 2nd ed. Cambridge, Pergamon (1997)
Radi E.: On the effects of characteristic lengths in bending and torsion on Mode III crack in couple stress elasticity. Int. J. Solids Struct. 45, 3033–3058 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lakes, R.S. Reduced warp in torsion of reticulated foam due to Cosserat elasticity: experiment. Z. Angew. Math. Phys. 67, 46 (2016). https://doi.org/10.1007/s00033-016-0632-4
Received:
Published:
DOI: https://doi.org/10.1007/s00033-016-0632-4